6. Prove that energy is a property of the system
Answers
Let us consider a cyclic process performed by the system
∫(δQ−δW)=∫2IA(δQ−δW)+∫2IC(δQ−δW)=0
in which the summation around the cyclic procedure has been divide into its component parts. Let us now consider a second cyclic process, that varies from the first in that the outward path is now B instead of A. Applying the First Law to this procedure, we acquire:
∫2IB(δQ−δW)+∫2IC(δQ−δW)=0
From examining the above two equations we see that
∫2IA(δQ−δW)=∫2IB(δQ−δW)
This illustrates that the integral of (δ Q - δ W) from state 1 to state 2 is similar for paths A and B. As these have been randomly selected, we say that the integral has similar value for any path between 1 and 2.
Representing ∫ δ Q by Q, the total heat transfer during the procedure from 1 to 2, and ∫ δ W by W, the total work during the similar change of state, we can say that (Q – W) has similar value for any path between 1 and 2. From the definition of energy, equation
Q–W=E2–E1
Therefore it is seen that (E2−E1) has similar value for any path among 1 and 2. This entails that the value of (E2−E1) based only on the end states. Which means that energy is a property of a system.
Step-by-step explanation:
